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NASA NTRS1973

Can oscillations grow in a sunspot umbra.

Umbral flashes and running penumbral waves have been attributed by Moore (1972) to overstable oscillations in the umbra. His numerical results were derived by inserting physical conditions at two particular depths beneath the umbral surface. Seven variables must be specified at each point. We have extended Moore's analysis to examine the depth-dependence of overstable oscillations in a recently computed umbral model. Electrical conductivity is evaluated taking full account of partial ionization and magnetic fields. In the surface layers, within 250 km of the top of the umbral convection zone, the conductivity is so low that Joule dissipation is more rapid than the growth rate of oscillations. In these layers, Moore's results are therefore not applicable. At greater depths, oscillations can grow and we agree with Moore that both umbral flashes and penumbral waves may be due to overstable oscillations. However, we suggest that both phenomena can arise at the same depth in the spot, and not in two layers, as Moore suggests.

Mullan, D. J.↗

NASA NTRS1989

Role of computational fluid dynamics in unsteady aerodynamics for aeroelasticity

In the last two decades there have been extensive developments in computational unsteady transonic aerodynamics. Such developments are essential since the transonic regime plays an important role in the design of modern aircraft. Therefore, there has been a large effort to develop computational tools with which to accurately perform flutter analysis at transonic speeds. In the area of Computational Fluid Dynamics (CFD), unsteady transonic aerodynamics are characterized by the feature of modeling the motion of shock waves over aerodynamic bodies, such as wings. This modeling requires the solution of nonlinear partial differential equations. Most advanced codes such as XTRAN3S use the transonic small perturbation equation. Currently, XTRAN3S is being used for generic research in unsteady aerodynamics and aeroelasticity of almost full aircraft configurations. Use of Euler/Navier Stokes equations for simple typical sections has just begun. A brief history of the development of CFD for aeroelastic applications is summarized. The development of unsteady transonic aerodynamics and aeroelasticity are also summarized.

Guruswamy, Guru P.↗

NASA NTRS1988

Simplified Analysis Of Shock Waves

Semiempirical expressions and conventional analyses agree within about 3 percent. Set of semiempirical formulas enables direct calculation of supersonic and hypersonic shock-wave parameters without use of iterative procedures. Formulas provided for calculating shock deflection angle and downstream static pressure and enthalpy over mach number range of 2 to 25. Relationship describing thermodynamic behavior of partially dissociated air also developed.

Neuenschwander, Wilmer E.↗

NASA NTRS1986

Mesospheric gravity-wave climatology at Adelaide

The MF Adelaide partial-reflection radar has been operating continuously since November 1983. This has enabled a climatology of gravity-wave activity to be constructed for the mesosphere. The data have been analyzed for a medium-period range of 1 to 8 hr. and a longer period range between 8 and 24 hr. covering the inertio-period waves. The tidal motions have been filtered out prior to analysis. For the data analyses so far (Nov. 1983 to Dec. 1984), a number of interesting features emerged. Firstly, the wave activity at heights above 80 km shows a small seimannual variation with season with the activity being strongest in summer and winter. At heights below 80 km however, there is a similar but more marked variation with the weakest amplitudes occurring at the time of the changeovers in the prevailing circulation. If breaking gravity waves are responsible for much of the turbulence in the mesosphere, then the periods March to April and September to October might also be expected to be periods of weak turbulence. The wave field appears to be partially polarized. The meridional amplitudes are larger than the zonal amplitudes, especially in water. It is found that the degree of polarization is about 15% in summer and 30% in winter. The polarized component is found to propagate in the opposite direction to the background flow in the stratosphere, which suggests that the polarization arises through directional filtering of the waves as they propagate up from below.

Vincent, R. A.↗

NASA NTRS2004

Variable Step Integration Coupled with the Method of Characteristics Solution for Water-Hammer Analysis, A Case Study

One-dimensional water-hammer modeling involves the solution of two coupled non-linear hyperbolic partial differential equations (PDEs). These equations result from applying the principles of conservation of mass and momentum to flow through a pipe, and usually the assumption that the speed at which pressure waves propagate through the pipe is constant. In order to solve these equations for the interested quantities (i.e. pressures and flow rates), they must first be converted to a system of ordinary differential equations (ODEs) by either approximating the spatial derivative terms with numerical techniques or using the Method of Characteristics (MOC). The MOC approach is ideal in that no numerical approximation errors are introduced in converting the original system of PDEs into an equivalent system of ODEs. Unfortunately this resulting system of ODEs is bound by a time step constraint so that when integrating the equations the solution can only be obtained at fixed time intervals. If the fluid system to be modeled also contains dynamic components (i.e. components that are best modeled by a system of ODEs), it may be necessary to take extremely small time steps during certain points of the model simulation in order to achieve stability and/or accuracy in the solution. Coupled together, the fixed time step constraint invoked by the MOC, and the occasional need for extremely small time steps in order to obtain stability and/or accuracy, can greatly increase simulation run times. As one solution to this problem, a method for combining variable step integration (VSI) algorithms with the MOC was developed for modeling water-hammer in systems with highly dynamic components. A case study is presented in which reverse flow through a dual-flapper check valve introduces a water-hammer event. The predicted pressure responses upstream of the check-valve are compared with test data.

Turpin, Jason B.↗

NASA NTRS1965

Wave-Plan Analysis of Unsteady Flow

An analytical method for computing unsteady flow conditions in liquid-filled flow systems is developed. The method which is called the wave plan incorporates distributed parameter and nonlinear effects including the effects of viscous resistance. The wave plan is essentially a solution synthesized from the effects of incremental step pressure pulses. The pressure pulses are generated because of incremental flow-rate changes that originate in a hydraulic system from a variety of sources, including the mechanical motion of the system structure. The pressure pulses propagate throughout the system at sonic velocity and are partially transmitted and reflected at each discontinuity. The velocity change caused by each pressure pulse is obtained from the Joukowski relation. Pressure and velocity time histories at any point in the system are obtained by a timewise summation of the contributions of the incremental pressure pulses passing that point. The analysis is presented in a form general enough to be applied to a variety of hydraulic systems. To illustrate the application of the method to a specific system, the response of a straight hydraulic line to a sinusoidal orifice-area variation of an upstream valve is computed. Both a constant-cross- section line and a tapered line are analyzed in the examples, and various nonlinear effects evaluated. Comparisons are carried out with experimental data obtained for the constant-diameter line and good agreement is shown to exist.

UNSTEADY FLOW↗

NASA NTRS1972

A simple Fourier analysis technique for measuring the dynamic response of manual control systems.

From a practical standpoint most dynamic response analysis techniques are complicated, expensive, and time consuming to mechanize and operate. Adaptive parameter tracking techniques partially overcome these faults, but they have prescribed forms which is an undesirable restriction for basic research. To overcome these drawbacks, an on-line Fourier analysis technique has been developed which deals only with the input and error signals in a manual feedback control system. Several sine waves are used for the input, and the on-line data measurement includes the error variance and a simple means for obtaining the sine and cosine transforms of the error signal at each of the input frequencies. From this relatively small amount of data, we show simple ways to compute the open- and closed-loop dynamic response at input frequencies and the relative amount of linearly correlated power in the error signal.

Allen, R. W.↗

NASA NTRS1994

On the dynamics of small-scale vorticity in isotropic turbulence

It was previously shown that the strong vorticity in isotropic turbulence is organized into tubular vortices ('worms') whose properties were characterized through the use of full numerical simulations at several Reynolds numbers. At the time most of the observations were kinematic, and several scaling laws were discovered for which there was no theoretical explanation. In the meantime, further analysis of the same fields yielded new information on the generation of the vortices, and it was realized that even if they had to be formed by stretching, they were at any given moment actually compressed at many points of their axes. This apparent contradiction was partially explained by postulating axial inertial waves induced by the nonuniformity of the vortex cores, which helped to 'spread' the axial strain and allowed the vortices to remain compact even if not uniformly stretched. The existence of such solutions was recently proved numerically. The present report discusses a set of new numerical simulations of isotropic turbulence, and a reanalysis of the old ones, in an effort to prove or disprove the presence of these waves in actual turbulent flows and to understand the dynamics, as opposed to the kinematics, of the vortices.

Jimenez, Javier↗

NASA NTRS1995

Investigation of computational and spectral analysis methods for aeroacoustic wave propagation

Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. Consequently, simulated waves propagate with the correct wave speeds and exhibit their appropriate properties. A set of radiation and outflow boundary conditions, compatible with the DRP scheme and derived from the asymptotic solutions of the governing equations, are also implemented. Numerical simulations are performed to test the effectiveness of the DRP scheme and its boundary conditions. The computed solutions are shown to agree favorably with the exact solutions. The major restriction appears to be that the dispersion relations can be preserved only for waves with wave lengths longer than four or five spacings. The boundary conditions are found to be transparent to the outgoing disturbances. However, when the disturbance source is placed closer to a boundary, small acoustic reflections start appearing. CAA generates enormous amounts of temporal data which needs to be reduced to understand the physical problem being simulated. Spectral analysis is one approach that helps us in extracting information which often can not be easily interpreted in the time domain. Thus, three different methods for the spectral analysis of numerically generated aeroacoustic data are studied. First, the capabilities of two traditional methods for spectral analysis, namely, the Blackman-Tukey method and periodogram method, are compared in estimating the spectra of a simple-periodic process. The periodogram is then applied to analyze transitory-deterministic processes. Finally, these two methods are compared with a more recent method, referred as the Weighted-Overlapped-Segment-Averaging (WOSA) method, in estimating the spectra of a chaotic (random-like) process. From the demonstrative case for the spectral analyses of data generated by simple-periodic process, the periodogram method is found to give a better estimate of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window is found to perform better with the periodogram method than with the Blackman-Tukey method. Finally, for the spectral analysis of data generated by the chaotic process, the periodogram method does not perform well, whereas, the WOSA and Blackman-Tukey methods give equivalently good results.

Vanel, Florence O.↗

NASA NTRS1960

Evaluation of Blended Wing-Body Combinations with Curved Plan Forms at Mach Numbers Up to 3.50

This investigation is a continuation of the experimental and theoretical evaluation of the effects of wing plan-form variations on the aerodynamic performance characteristics of blended wing-body combinations. The present report compares previously tested straight-edged delta and arrow models which have leading-edge sweeps of 59.04 and 70-82 deg., respectively, with related models which have plan forms with curved leading and trailing edges designed to result in the same average sweeps in each case. All the models were symmetrical, without camber, and were generally similar having the same span, length, and aspect ratios. The wing sections had an average value of maximum thickness ratio of about 4 percent of the local wing chords in a streamwise direction. The wing sections were computed by varying their shapes along with the body radii (blending process) to match the selected area distribution and the given plan form. The models were tested with transition fixed at Reynolds numbers of roughly 4,000,000 to 9,000,000, based on the mean aerodynamic chord of the wing. The characteristic effect of the wing curvature of the delta and arrow models was an increase at subsonic and transonic speeds in the lift-curve slopes which was partially reflected in increased maximum lift-drag ratios. Curved edges were not evaluated on a diamond plan form because a preliminary investigation indicated that the curvature considered would increase the supersonic zero-lift wave drag. However, after the test program was completed, a suitable modification for the diamond plan form was discovered. The analysis presented in the appendix indicates that large reductions in the zero-lift wave drag would be obtained at supersonic Mach numbers if the leading- and trailing-edge sweeps are made to differ by indenting the trailing edge and extending the root of the leading edge.

Holdaway, George H.↗

NASA NTRS1993

A hybrid finite element-boundary integral for the analysis of cavity-backed antennas of arbitrary shape

This is the final report on this project which was concerned with the analysis of cavity-backed antennas and more specifically spiral antennas. The project was a continuation of a previous analysis, which employed rectangular brick elements, and was, thus, restricted to planar rectangular patch antennas. A total of five reports were submitted under this project and we expect that at least four journal papers will result from the research described in these reports. The abstracts of the four previous reports are included. The first of the reports (028918-1-T) is over 75 pages and describes the general formulation using tetrahedral elements and the computer program. Report 028918-2-T was written after the completion of the computer program and reviews the capability of the analysis and associated software for planar circular rectangular patches and for a rectangular planar spiral. Measurements were also done at the University of Michigan and at Mission Research Corp. for the purpose of validating the software. We are pleased to acknowledge a partial support from Mission Research Corp. in carrying out the work described in this report. The third report (028918-3-T) describes the formulation and partial validation (using 2D data) for patch antennas on a circular platform. The 3D validation and development of the formulation for patch antennas on circular platforms is still in progress. The fourth report (028918-4-T) is basically an invited journal paper which will appear in the 'J. Electromagnetic Waves and Applications' in early 1994. It describes the application of the finite element method in electromagnetics and is primarily based on our work here at U-M. This final report describes the culmination of our efforts in characterizing complex cavity-backed antennas on planar platforms. The report describes for the first time the analysis of non-planar spirals and non-rectangular slot antennas as well as traditional planar patch antennas. The comparisons between measurements and calculations are truly impressive. Another unique aspect of this work is the incorporation of the FFT as part of the BiCG solver by overlaying a structured triangular mesh over the unstructured mesh. The implementation of this BiCG-FFT solution algorithm is important in minimizing the CPU and storage requirements. This final report will be submitted for publication in a refereed journal.

Gong, Jian↗

NASA NTRS1971

Probing atmospheric water vapor profiles via multiple scattering of electromagnetic waves

A theoretical analysis on the multiple scattering of electromagnetic waves propagating in a finite inhomogeneous medium is presented and applied to the study of wave propagation in a clear atmosphere (fine weather conditions). It is shown that the analysis offers a method of synthesizing the water vapor density profile in a clear atmosphere by measuring the resultant reflections from the density profile at several different frequencies. It is also shown that the resultant reflection emerges as the consequence of multiple scattering of partial reflections from various parts of the inhomogeneous medium. The solutions of the multiple scattering approach are shown to be more accurate than those of the WKB approach, which neglects the multiple scattering effects.

Tang, C. C. H.↗

NASA NTRS2001

Advanced Methods for Aircraft Engine Thrust and Noise Benefits: Nozzle-Inlet Flow Analysis

Three connected sub-projects were conducted under reported project. Partially, these sub-projects are directed to solving the problems conducted by the HU/FM&AL under two other NASA grants. The fundamental idea uniting these projects is to use untraditional 3D corrugated nozzle designs and additional methods for exhaust jet noise reduction without essential thrust lost and even with thrust augmentation. Such additional approaches are: (1) to add some solid, fluid, or gas mass at discrete locations to the main supersonic gas stream to minimize the negative influence of strong shock waves forming in propulsion systems; this mass addition may be accompanied by heat addition to the main stream as a result of the fuel combustion or by cooling of this stream as a result of the liquid mass evaporation and boiling; (2) to use porous or permeable nozzles and additional shells at the nozzle exit for preliminary cooling of exhaust hot jet and pressure compensation for non-design conditions (so-called continuous ejector with small mass flow rate; and (3) to propose and analyze new effective methods fuel injection into flow stream in air-breathing engines. Note that all these problems were formulated based on detailed descriptions of the main experimental facts observed at NASA Glenn Research Center. Basically, the HU/FM&AL Team has been involved in joint research with the purpose of finding theoretical explanations for experimental facts and the creation of the accurate numerical simulation technique and prediction theory for solutions for current problems in propulsion systems solved by NASA and Navy agencies. The research is focused on a wide regime of problems in the propulsion field as well as in experimental testing and theoretical and numerical simulation analysis for advanced aircraft and rocket engines. The F&AL Team uses analytical methods, numerical simulations, and possible experimental tests at the Hampton University campus. We will present some management activity and theoretical numerical simulation results obtained by the FM&AL Team in the reporting period in accordance with the schedule of the work.

Morgan, Morris H.↗

NASA NTRS1981

Simple approximations for the asymptotic description of the interaction between a normal shock wave and a turbulent boundary layer at transonic speeds

The asymptotic description of the interaction between a normal shock wave and a turbulent boundary layer is reviewed. The layers necessary in a rational analysis of the interaction are discussed with emphasis on the differences from an interaction with a laminar boundary layer, the uncoupling of solutions for the distribution of pressure and skin friction at the wall, and the role of the Reynolds shear stress in these solutions. The accuracy of asymptotic solutions in flows at Reynolds numbers of technical interest is discussed. Solutions for the distribution of pressure and skin friction at the wall and the shape of the shock are considered for the case where the flow is near separation. For the pressure and skin friction, it is possible to write two simplified partial solutions, one valid at the beginning of the interaction and one valid somewhat downstream of the shock wave. A solution composed of these two parts and a linear interpolation between them appears to give good comparison with experiment; one unknown constant, independent of the parameters of the interaction, must be found from experiment. The simplified relations are presented. Comparison of numerical computations with experimental data indicates a possible value for the constant and shows quite satisfactory results.

Adamson, T. C., Jr.↗

NASA NTRS1977

On two-dimensional packets of capillary-gravity waves

The motion of a two-dimensional packet of capillary-gravity waves on water of finite depth is studied. The evolution of a packet is described by two partial differential equations: the nonlinear Schroedinger equation with a forcing term and a linear equation, which is of either elliptic or hyperbolic type depending on whether the group velocity of the capillary-gravity wave is less than or greater than the velocity of long gravity waves. These equations are used to examine the stability of the Stokes capillary-gravity wave train. The analysis reveals the existence of a resonant interaction between a capillary-gravity wave and a long gravity wave. The interaction requires that the liquid depth be small in comparison with the wavelength of the (long) gravity waves and the evolution equations describing the dynamics of this interaction are derived.

Djordjevic, V. D.↗

NASA NTRS1994

Mean motions and tidal and two-day structure and variability in the mesosphere and lower thermosphere over Hawaii

An overview of the motion field and an analysis of the tidal and 2-day wave motions observed in the mesosphere and lower thermosphere over the central Pacific from 1 October 1990 through 19 August 1992 is presented. Characteristics and interactions of motions at lower and higher frequencies will be addressed elsewhere. Wind measurements were obtained with an MF radar operating on Kauai, Hawaii (22 deg N, 160 deg W), using the partial reflection drift technique. Results presented in this paper reveal a zonal mean motion reflecting the mesopause semiannual oscillation (MSAO) observed at more equatorial latitudes from approximately January to July, coinciding with the period during which the MSAO and the annual cycle of the zonal mean wind at higher latitudes are in phase. Eastward and westward maxima are 55 m/s below 80 km and 45 m/s near 85 km during the first year, with maxima of 57 and 53 m/s during the second year and evidence of substantial interannual variability. The second MSAO cycle is greatly suppressed in the Hawaiian data due to the reversal of the correlation between this and the annual cycle at higher latitudes from approximately July to December and because the second cycle is weaker climatologically at equatorial latitudes. Significant planetary wave activity is observed during periods of mean eastward motions, and tidal and 2-day motions are found to be large and variable. The maximum diurnal tides were observed during October and November 1990, and February, March, April, July, and August of 1991 and 1992. Maximum 2-day amplitudes occurred during February, July, and August of 1991 and 1992. Significantly, the large diurnal amplitude maximum noted during November 1990 failed to appear the following year, while the February 2-day amplitude maximum declined somewhat in 1992.

Fritts, David C.↗

NASA NTRS1994

The Fraternal Twins of Quartet O4(+)

Eleven stationary geometries of quartet O4(+) have been studied by ab initio methods. The geometries were optimized at the Complete Active Space Self-Consistent Field (CASSCF) level of theory and the energies were calculated by the multiconfigurational second order pertubation method (CASPT2), using Double-Zeta Plus polarization (DZP), Triple-Zeta Plus Double Polarization (TZ2P), average Atomic Natural Orbital (ANO) (5s4p2d) and average ANO (6s5p3d2f) basis sets. The rectangular and trans-planar structures are found to be the most stable, with an energy barrier to conversion between the two at the threshold of dissociation. Both have a delocalized hole and are stable relative to separated 02 and 02(+)by 11.0 and 11.5 kcal/mol for the rectangular and the 2 trans-planar structure, respectively, compared with the experimentally deduced energy in the range of 9.2 to 10.8 kcal/mol. The adiabatic ionization potentials of 04 and 02 are computed to be 11.67 and 12.21 eV, while experimental values are 11.66 and 12.07 eV, respectively. The vibrational frequencies have been computed for all degrees of freedom at the CASSCF level of theory. Symmetry breaking is found to be a particular problem in the computation of the antisymmetric stretch frequency for the delocalized structures at the CASSCF level of theory. Attempts to rectify these problems using the restricted active space self-consistent field (RASSCF) method leads to additional difficulties, but further analysis yields insight into the symmetry breaking and problems with earlier calculations. Finally, a nonorthogonal configuration interaction (CI) calculation based on the interaction of localized CASSCF wave functions using the Complete Active Space State Interation (CASSI) method leads to a balanced treatment of the antisymmetric stretch which is free from symmetry breaking. The study explains the four most prominent absorption frequencies observed in the partially unassigned IR spectrum of O4(+) isolated in solid neon as the antisymmetric OO stretch, and the combination band of the symmetric and antisymmetric 00 stretch of both the rectangular and trans-planar structures.

Lindh, Roland↗

NASA NTRS2002

Higher Order Bases in a 2D Hybrid BEM/FEM Formulation

The advantages of using higher order, interpolatory basis functions are examined in the analysis of transverse electric (TE) plane wave scattering by homogeneous, dielectric cylinders. A boundary-element/finite-element (BEM/FEM) hybrid formulation is employed in which the interior dielectric region is modeled with the vector Helmholtz equation, and a radiation boundary condition is supplied by an Electric Field Integral Equation (EFIE). An efficient method of handling the singular self-term arising in the EFIE is presented. The iterative solution of the partially dense system of equations is obtained using the Quasi-Minimal Residual (QMR) algorithm with an Incomplete LU Threshold (ILUT) preconditioner. Numerical results are shown for the case of an incident wave impinging upon a square dielectric cylinder. The convergence of the solution is shown versus the number of unknowns as a function of the completeness order of the basis functions.

Fink, Patrick W.↗